The equation of a circle $C$ is $x^2+y^2-8y-9 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2) + (y^2-8y) = 9$ $(x^2) + (y^2-8y+16) = 9 + 0 + 16$ $x^2 + (y-4)^{2} = 25 = 5^2$ Thus, $(h, k) = (0, 4)$ and $r = 5$.